Studies have suggusted that twins, in their early years, tend to have lower IQs
ID: 3155934 • Letter: S
Question
Studies have suggusted that twins, in their early years, tend to have lower IQs and pick up language more slowly than nontwins. The slower intellectual growth might be caused by benign parental neglect. Suppose it is desired to estimate the mean attention time given to twins per week by their parents. A sample of 70 sets of 2 year old boys is taken, and after 1 week the attention time recieved was recorded. The data (in hours) calculated the mean at 21 and the standard deviation at 10.7. Use this information to contruct a 90% confidence interval for the mean attention time given to al twin boys by their parents. Find margin or error and confidence interval.
Explanation / Answer
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 21
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 10.7
n = sample size = 70
Thus,
Margin of Error E = 2.103594441 [ANSWER]
Lower bound = 18.89640556
Upper bound = 23.10359444
Thus, the confidence interval is
( 18.89640556 , 23.10359444 ) [ANSWER]